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Here is a start of a Wiki called “Math Future” (not “math 2.0″ since it’s somewhat silly, and also in case we progress beyond 2.0) http://mathfuture.wikispaces.com/ There, you can add events you organize or attend to the calendar, tell people about your projects, find collaborators, and work toward some common language (math 2.0, math social objects, learning disintermediation and so on).

Twitter chats will be on Wednesdays, July 15th, 6-7pm Pacific / 9-10pm Eastern, with #mathchat tag used. Please volunteer yourself or colleagues to host! I’d like to see 5-7 rotating hosts. This Wednesday, Colleen King of Math Playground (@colleenk) and I (@mariadroujkova) will host it.

Diigo group we will use is Math Links with “Math 2.0″ tag. If any of your bookmarks relate to the topic, can you please add “Math 2.0″ (in quotations) to them? To add tags to other members’ links, click “save” and then select “save to the group” option.

LearnCentral events will start in August (the NECC debriefing is still going strong).

At a Math Club, we were working with paper punches and folding. Symmetry of all sorts was on everybody’s minds. A. (4) drew a unicorn with two legs. We all started to ask about it, and she said: “It has two legs on this side and two on the other side!” Then she turned the paper over and drew two legs on the other side - on the other side of the paper!

Once the tree is built, it can be used for several activities. Start from common words, gradually moving to mathematical terms:

• How many grandparents are there? (point to the “grandparent” level on the tree). What about great-grandparents?
• We have one child, and we have two parents in the first generation from the child, and four grandparents in the second generation, and eight great-grandparents in the third generation… How many people are in the fourth generation? Fifth? How do you know?
• Mathematicians use the term “power” here. For example, we can say “grandparents” or “the second generation from the child” or “two to the second power.” Two to the first power (parents) is two. Two to the second power (grandparents) is eight. What is two to the third power? There is a symbol for it:

  2³=8

• What generation has eight people? What power of two makes sixteen?
  Figuring out which generation each quantity means is a lot like logarithms.
  We can say, “What generation has sixteen people?” or we can write:
  log₂16=4
• Add up all generations up to a certain level, say, “grandparents”. Compare to the number in the next level. What do you observe? Is it always the case?

(by CommLab )

- Rapid prototyping of everything, short cycles of evaluation and change, and correspondingly short educational experiences are the norm. Families have moved from “package deal” of whole set curricula (”this is what you do for middle school”) to hand-picking books, teachers, and methods for each child for each 2-4 months of each subject. A kid can stay with a program that works for years, or drop one that does not in a few weeks. This leads to increased quality of programs.

(by Oakland Community College)

- High value is placed on engagement, love for subjects and personal relevance of activities both for activity leaders and for all participants. It is expected that participants and especially leaders of activities CARE. Children are much more likely to be learning topics and subjects that are meaningful for them personally, in ways they personally find engaging. Much discussion happens, and much know-how is accumulated about ways of finding and developing meaningful activities for particular subject areas.

- Deconstruction of “age” and shift to ability levels and styles is frequent among homeschoolers. One often sees age spreads of 3-6 years within each homeschool group activity. Grouping by age is rare and loose (e.g. “teens and tweens” rather than “fourteen year olds”). Correspondingly, friendships and informal communities form across ages, based on common interests and activities.

(by iTunes U)

- Barter economies, gift economies, network economies, coops and other innovative (or age-old) alternative forms of education financing are widespread. Homeschoolers value and often use open and free software and open educational resources, as well as the culture of exchange and communal use of resources. Interestingly, the largest benefits of homeschooling as far as standardized tests and college admissions go happen in the poorest families with lowest-educated parents.

(by Turno)

- Co-production models of learning, where learners and teachers are curriculum co-creators, project learning, unit studies and other active learning models are prevalent among homeschoolers.

- Homeschoolers often form “nakama” groups, small, local tight friend and family groups getting together to achieve their goals, and tied personally as well as educationally. High value is placed on friendships, and day-to-day educational decisions come from these personal ties.

- There are active, robust local communities and global support networks for homeschooling families, for anything from finding an appropriate math program for highly gifted ADHD Asperger kid who likes computers, to helping a family through tough economic times. Homeschoolers are some of the most socially networked demographics, which include lightning-fast spread of politically relevant news, such as proposed laws.

I think of homeschoolers as a distributed think tank and early adopters of education practices of the future.

My comment to USA Today article at http://www.usatoday.com/news/education/2009-05-28-homeschooling_N.htm

1. Hashtag aggregation for topical conversations at online events, conferences and so on
2. A way to communicate about face-to-face events as they go on, with other attendees, without breaking up the oral presentations flow
3. Ongoing conversations about particular topics with “whoever may tune in” - check out #math for example or #educhat
4. Aggregation of tweets for web sites or blogs using widgets
5. News: all global and most local events are trending, and often you can learn personal information from participants
6. Learning what colleagues are doing, such as events, conferences, projects, meetings, communal documents. Following people I like to their events, which tend to be interesting because these interesting people choose to participate.
7. Quickly publishing my short thoughts before they go away. This promotes creativity, somehow. People should seriously look into the effect.
8. The feeling of being close with colleagues. It’s like living in a small town and bumping into someone at the grocer’s and the drug store and the park. You communicate with the same person on LinkedIn and their blog and then Twitter too, and it strengthens the neighborly feelings.

Here is an excellent presentation by Tom Barrett, or @tombarrett:

And here is a cute cartoon on some of Twitter dangers:

And here is a great blog post on using backchannels, including Twitter, for your events, from TwitTip.

Update: a clever way to use Twitter to support doctoral dissertation writing!

This parking meter is a contribution to What Can You Do With This, or WCYDWT, project. Dor Abrahamson sent it to me, together with this story for WCYDWT people:

“I’m co-teaching w/ Prof. Alan Schoenfeld an undergraduate course for future teachers, at UC Berkeley. It’s a problem-solving based course, and the problems are often based on mundane situations. We used this authentic document - a Berkeley parking meter - to explore multiplicative structure and rational numbers. Rate, I guess. Basically, we show this picture and ask what the best bang for the buck is. To our great surprise there was much confusion in terms of concepts, notation, vocabulary. Diverse approaches, some we couldn’t make sense of.

Judging by your blog, I need not demonstrate what a talented math teacher could do with this material. The mind reels, right? One of the interesting angles here is that some kids calculate min/cent, and others go for cent/min. We all wish to equalize the “denominator” so that we can compare the “numerators” directly. However, for me the min/cent feels intuitive, b/c I want to know how much bang I get for the buck. And yet, think of those ‘value’ numbers we see in the supermarket, which help us choose between comparable products that come in different volumes — they tell you, e.g,. 39c/ounce. So the equivalent here would be cent/min, right?

And so on. We played with polynomials so as to figure out what exact minute totals we could produce and how much they would cost us.

Time is money.

Oh, and the person whose image we can just discern in the display area of the parking meter is Becky Blessing — this is her, errr, reflection piece.”

UPDATE: Becky already submitted this picture in February, and there is a very nice discussion there at dy/dan blog.

The future is already here, it’s just not evenly distributed. The future where toddlers and their parents play with algebraic ideas, where kids contribute to real work as apprentices, where everybody is able to create or improve mathematical conjectures, definitions and metaphors. We are working on inviting more and more people to work and play in this future, now. This mind map shows some of our tools.

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